Explanation:
When two circles intersect at two distinct points, there are two possibilities for the number of common tangents: either 2 or 4. Let's consider each possibility in detail.

Possibility 1: 2 common tangents
In this case, the two circles are externally tangent to each other. This means that the circles touch each other at a single point from the outside. When two circles are externally tangent, there are two common tangents that can be drawn: one from the point of tangency to the other side of each circle. These tangents are external to both circles and do not intersect each other. Therefore, the maximum number of common tangents is 2.

Possibility 2: 4 common tangents
In this case, the two circles are internally tangent to each other. This means that one circle is fully contained inside the other circle, and they touch each other at a single point from the inside. When two circles are internally tangent, there are four common tangents that can be drawn: two internal tangents and two external tangents.

- The internal tangents are drawn from the point of tangency to the other side of each circle. These tangents are inside both circles and do not intersect each other.
- The external tangents are drawn from the point of tangency to the other side of each circle. These tangents are outside both circles and do not intersect each other.

Therefore, the maximum number of common tangents is 4.

Conclusion:
In the given scenario, where two circles intersect at two distinct points, the maximum number of common tangents that can be drawn is 2.